Precision positioning system using a wavelength tunable laser

Abstract

A method for determining characteristics of a test cavity, the method includes for each of a plurality of optical frequencies within a bandwidth of a tunable laser, measuring interference signals from the test cavity and a reference cavity having a known characteristic. The method includes determining values for the plurality of optical frequencies from the measured interference signals from the reference cavity and the known characteristic of the reference cavity, and determining the characteristic of the test cavity using the determined values of the plurality of optical frequencies.

What is claimed is: 
     
       1. A method for determining a characteristic of a test cavity, the method comprising:
 for each of a plurality of optical frequencies within a bandwidth of a tunable laser, measuring interference signals from the test cavity and a reference cavity having a known characteristic; 
 determining values for the plurality of optical frequencies from the measured interference signals of the reference cavity and the known characteristic of the reference cavity, and 
 determining the characteristic of the test cavity using the determined values of the plurality of optical frequencies, 
 wherein measuring the interference signals comprises sweeping through the plurality of optical frequencies within the bandwidth of the tunable laser as a function of time and measuring the interference signals for both the test cavity and the reference cavity for each of multiple, different times during the sweeping so that the measured signals for the test and reference cavities at each of the multiple, different times correspond to different ones of the plurality of optical frequencies within the bandwidth of the tunable laser. 
 
     
     
       2. The method of  claim 1 , wherein determining the values for the plurality of optical frequencies is based on an initial estimate for the plurality of optical frequencies. 
     
     
       3. The method of  claim 2 , wherein a single reference cavity is used and the plurality of optical frequencies is known to within half of a free spectral range of the reference cavity. 
     
     
       4. The method of  claim 1 , wherein an error in the determined characteristic of the test cavity caused by uncertainty in the values for the plurality of optical frequencies is reduced. 
     
     
       5. The method of  claim 1 , wherein the characteristic comprises a gap size within the test cavity, the reference cavity comprises a fixed reference cavity, and the known characteristic of the reference cavity comprises a gap size of the fixed reference cavity. 
     
     
       6. The method of  claim 1 , further comprising determining a second characteristic of the test cavity, the second characteristic comprises a velocity of the test cavity. 
     
     
       7. The method of  claim 1 , wherein initial values for the plurality of optical frequencies are known to within half of a free spectral range of the reference cavity, and the values for the plurality of optical frequencies are determined directly from the interference signals of the reference cavity. 
     
     
       8. The method of  claim 1 , wherein determining the characteristic of the test cavity using the determined values of the plurality of optical frequencies comprises using phase analysis of multiple overlapping segments within the plurality of optical frequency, each segment containing data points that cover a portion of the plurality of optical frequencies within the bandwidth of the tunable laser. 
     
     
       9. The method of  claim 8 , wherein a velocity of the test cavity is constant within a sampling of the data points in the segment. 
     
     
       10. A method for determining a characteristic of a test cavity, the method comprising:
 for each of a plurality of optical frequencies within a bandwidth of a tunable laser, measuring interference signals from the test cavity and a reference cavity having a known characteristic; 
 determining values for the plurality of optical frequencies from the measured interference signals of the reference cavity and the known characteristic of the reference cavity, and 
 determining the characteristic of the test cavity using the determined values of the plurality of optical frequencies, 
 further comprising measuring interference signals from a second reference cavity having a second known characteristic, wherein determining the values for the plurality of optical frequencies comprises fitting the measured interference signals of the reference cavity and the second reference cavity obtained for each of the plurality of optical frequencies within the bandwidth of the tunable laser to a mathematical model based on the known characteristics of the reference cavity and the second reference cavity, the reference cavity and the second reference cavity having different gap sizes. 
 
     
     
       11. The method of  claim 10 , wherein fitting the measured interference signals of the reference cavity and the second reference cavity comprises using regression analysis of the interference signals to a mathematical model to determine the values for the plurality of optical frequencies. 
     
     
       12. The method of  claim 11 , wherein the mathematical model comprises an analytical function. 
     
     
       13. The method of  claim 11 , wherein determining the values for the plurality of optical frequencies comprises using Gauss-Newton optimization. 
     
     
       14. The method of  claim 11 , wherein determining the values for the plurality of optical frequencies comprises using Gauss-Newton optimization, and determining a Jacobian of partial derivatives of the measurement interference signals with respect to the optical frequency based on the analytical function. 
     
     
       15. An interferometry system for characterizing a test cavity, the system comprising:
 a reference cavity having a known characteristic; 
 a tunable laser having a plurality of optical frequencies within a bandwidth; 
 optical elements to direct each of the plurality of optical frequencies within the bandwidth of the tunable laser to the test cavity and the reference cavity; 
 an acquisition system configured to be synchronized to the tunable laser to obtain measured interference signals from the reference cavity and the test cavity at each of the plurality of optical frequencies; and 
 an electronic processor coupled to the acquisition system to receive the interference signals, and configured to determine values for the plurality of optical frequencies from the measured interference signals and the known characteristic, 
 and wherein the acquisition system is configured to cause the tunable laser to sweep through the plurality of optical frequencies within the bandwidth of the tunable laser as a function of time and further configured to obtain the measured interference signals for both the test cavity and the reference cavity for each of multiple, different times during the sweeping so that the measured signals for the test and reference cavities at each of the multiple, different times correspond to different ones of the plurality of optical frequencies within the bandwidth of the tunable laser. 
 
     
     
       16. The interferometry system of  claim 15 , wherein the electronic processor is further configured to determine a characteristic of the test cavity based on the measured interference signals for the test cavity. 
     
     
       17. The system of  claim 15 , wherein the reference cavity has a confocal design to minimize dispersion. 
     
     
       18. The system of  claim 15 , wherein the values of the plurality of optical frequencies determined by the electronic processor has an uncertainty of less than 20 MHz for a tunable laser having a root-mean-square optical frequency variation of about 350 MHz. 
     
     
       19. The system of  claim 15 , wherein the electronic processor is configured to determine a characteristic of the test cavity using the determined values of the plurality of optical frequencies and phases extracted from data of multiple overlapping segments within the plurality of optical frequency, each segment containing data points that cover a portion of the plurality of optical frequencies within the bandwidth of the tunable laser. 
     
     
       20. An interferometry system for characterizing a test cavity, the system comprising:
 a reference cavity having a known characteristic; 
 a tunable laser having a plurality of optical frequencies within a bandwidth; 
 optical elements to direct each of the plurality of optical frequencies within the bandwidth of the tunable laser to the test cavity and the reference cavity; 
 an acquisition system configured to be synchronized to the tunable laser to obtain measured interference signals from the reference cavity and the test cavity at each of the plurality of optical frequencies; and 
 an electronic processor coupled to the acquisition system to receive the interference signals, and configured to determine values for the plurality of optical frequencies from the measured interference signals and the known characteristic, 
 further comprising one or more additional reference cavities having known characteristics, 
 wherein the acquisition system is configured to obtain measured interference signals from a second one of the one or more additional reference cavities, and 
 wherein the electronic controller is configured to determine the values for the plurality of optical frequencies by fitting the measured interference signals of the reference cavity and the second reference cavity obtained for each of the plurality of optical frequencies within the bandwidth of the tunable laser to a mathematical model based on the known characteristics of the reference cavity and the second reference cavity, the reference cavity and the second reference cavity having different gap sizes. 
 
     
     
       21. The system of  claim 20 , further comprises an intensity monitor to compensate for high speed laser intensity fluctuations in the tunable laser. 
     
     
       22. The system of  claim 20 , further comprising a fiber distributor configured to distribute light from a tunable laser to the reference cavity and the test cavity, wherein the test cavity is remotely positioned from the fiber distributor.